10d6 vs. 10‑Cards Bell Curve

11d6 vs. 11‑Cards Bell Curve

12d6 vs. 12‑Cards Bell Curve

A method that works fairly well is to use a deck of cards instead of dice. The
simplest way is to make a deck of 216 cards, each labeled with one of the 216
possible results you can roll on 3d6. You can also write in the 36 possible
results on 2d6, doing that six times, and the 6 possible results for 1d6, doing
that 36 times. This will allow a 216 card deck correctly simulate a roll of 1d6,
2d6, or 3d6 with perfect accuracy. However, 216 cards is a fairly large deck of
cards to handle and shuffle, and to keep it perfectly accurate you'd need to
reshuffle it after every die roll. It is certainly too large of a deck to be
convieniently used in a traveling situation, such as on a bus or car ride.

20-Card Deck

Qty.

Card

1

0 (Joker)

2

1's (Ace)

3

2's

4

3's

4

4's

3

5's

2

6's

1

7

Another method I hit on is to build a
smaller deck of just 20‑cards (thanks to a
discussion on GURPS Forums, and in
particular thanks to Brandy).
You can build that 20‑card deck by taking cards numbered 0 to 7, in quantities
from 1 to 4 (see table to the right); this small deck can be built using a deck
of standard playing cards, using a Joker or face card for the zero and two Aces
for the ones. When you make a die roll you simply draw a number of cards equal to the number of
dice that need to be rolled and add them together. The resulting bell curve
from this 20‑card deck is amazingly close to the bell curve of rolling
3d6, and is very close for 2d6 and 4d6. It is close enough for rolling 1d6 or
for rolling more dice, up to 6d6, and will yield fair result with the same
average and a similar shaped bell curve – tending more heavily
towards the average the more cards you draw – even for rolls such as 9d6 or 12d6.

For
1d6 you could keep a separate pile of cards numbered 1-6 to draw from,
but this precludes using one standard playing card deck. Another option is to
use the 20 card deck, but place 1-6 all in spades, with the 0 and 7, and all other cards,
as another suit. To roll 1d6 you simply draw from the
deck until you draw a spade.

At any rate, the draw deck will give a few odd
results which you will need to decide how to deal with. You can draw a result of
2 and 19 on 3d6. For skill rolls these should just be treated as a 3 and 18,
respectively. For damage rolls you will need to decide whether to threat them as
the actual result drawn or to normalize them to 3 and 18. Personally I
recommend just leaving them as the result drawn. Similarly, on 1d6 you can
draw a 0 or 7, and on 2d6 you can draw a 1 or 13. Again,
since these will always be damage rolls I recommend just leaving them as the
result that was drawn.